Convergence of Runge-Kutta-based convolution quadrature for semilinear fractional differential equations

For solving the semilinear fractional differential equations with the nonsmooth force term, we construct a class of Runge-Kutta-based convolution quadrature. Moreover, we analyse the convergence of the proposed scheme. In addition, we employ the fast Runge-Kutta approximation to reduce the calculation cost. Finally, we give some numerical experiments to verify the theoretical results.